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%\section*{Executive Summary}
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{\bf Executive Summary}
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In the Fall of 1999, the Fermilab Directorate chartered a study group
to investigate the physics motivation for a \textit{neutrino factory}
based on a muon storage ring that would operate in the era beyond the
current set of neutrino-oscillation experiments. We were charged to
evaluate the prospective physics program as a function of the stored
muon energy (up to $50\hbox{ GeV}$), the number of useful muon decays
per year (in the range from $10^{19}$ to $10^{21}$ decays per year),
and the distance from neutrino source to detector.
A companion study
evaluated the technical feasibility of a neutrino factory and
identified an R\&D program that would lead to a detailed design.
Our conclusion is that there is a compelling physics case for a
neutrino factory with a beam energy of about 20~GeV or greater,
that initially provides at least O($10^{19}$) muon decays per year.
The principal motivation for a neutrino factory is to provide the
intense, controlled, high-energy beams that will make possible
incisive experiments to pursue the mounting evidence for neutrino
oscillations. The composition and spectra of intense neutrino beams
from a muon storage ring will be determined by the charge, momentum,
and polarization of the stored muons, through the decays $\mu^{-}
\rightarrow e^{-}\nu_{\mu}\bar{\nu}_{e}$ or $\mu^{+} \rightarrow
e^{+}\bar{\nu}_{\mu}\nu_{e}$. There is no other comparable source of
electron neutrinos and antineutrinos.
In addition, a neutrino factory would provide well collimated
muon neutrino and antineutrino beams with energy spreads characteristic
of conventional narrow band beams. If the neutrino factory energy
exceeds about 20~GeV the neutrino beam intensity greatly exceeds
the corresponding intensity provided by conventional wide band beams.
The neutrino factory therefore offers
unprecedented opportunities for precise measurements of nucleon
structure and of electroweak parameters. The intense muon source
needed for the neutrino factory would make possible exquisitely
sensitive searches for muon-electron conversion and other rare
processes.
Experiments carried out at a neutrino factory within the next decade
can add crucial new information to our understanding of neutrino
oscillations. By studying the oscillations of $\nu_{\mu}$, $\nu_{e}$,
$\bar{\nu}_{\mu}$, and $\bar{\nu}_{e}$, it will be possible to
measure, or put stringent limits on, all of the appearance modes
$\nu_e \rightarrow \nu_\tau$, $\nu_e \rightarrow \nu_\mu$, and
$\nu_\mu \rightarrow \nu_\tau$. This is a necessary step beyond
the measurements provided by the next generation of neutrino
experiments, and will provide a basic test of
our understanding of neutrino oscillations. It will also
be possible to determine precisely (or place
stringent limits on) all of the leading oscillation parameters,
including the mixing angle $\theta_{13}$ which appears to be
difficult to determine precisely with conventional neutrino beams.
In addition, a neutrino factory would enable us to
infer the pattern of neutrino masses; and, under the right
circumstances, to observe \textsf{CP} violation in the lepton sector.
Baselines greater than about 2000~km will enable a quantitative study
of matter effects and a determination of the mass hierarchy. If the
Mini\textsc{BooNE} experiment confirms the $\nu_{\mu} \leftrightarrow
\nu_{e}$ effect reported by the LSND experiment, experiments with
rather short baselines (a few tens of km) could be extremely
rewarding, and enable, for example, the search for
$\nu_e \rightarrow \nu_\tau$ oscillations.
\begin{figure}
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\centerline{
\epsffile{summary_cp.eps}}
\caption{Predicted ratios of
$\bar\nu_e \to \bar\nu_\mu$ to $\nu_e \to \nu_\mu$
rates at a 20~GeV neutrino factory.
The upper (lower) band
is for $\delta m^2_{32} < 0$ ($\delta m^2_{32} > 0$).
The range of possible \textsf{CP} violation determines
the widths of the bands.
The statistical error shown corresponds to
$10^{20}$ muon decays of each sign and a 50~kt detector.
Results are from Ref.~\ref{bgrw00}.
}
\label{fig:summary_cp}
\end{figure}
\begin{figure}
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\centerline{
\epsffile{summary_all.eps}}
\caption{The required number of muon decays needed in a
neutrino factory to observe $\nu_e \rightarrow \nu_\mu$
oscillations in a 50~kt detector and determine the sign of $\delta m^2$,
and the number of decays needed to observe
$\nu_e \rightarrow \nu_\tau$ oscillations in a few~kt detector,
and ultimately
put stringent limits on (or observe) \textsf{CP} violation in the
lepton sector with a 50~kt detector.
Results are from Ref.~\ref{bgrw00}.}
\label{fig:summary_all}
\end{figure}
If the atmospheric neutrino deficit
is correctly described by three flavor oscillations with
$\delta m^2$ in the range favored by the SuperKamionkande
data, and if the parameter $\sin^2 2\theta_{13}$ is not
smaller than $\sim 0.01$, then exciting cutting--edge
long baseline oscillation physics could begin with an
$\sim50$~kt detector at a
neutrino factory with muon energies as low as 20~GeV
delivering as few as $10^{19}$ muon decays per year.
This ``entry--level" facility would be able to measure
$\nu_e \rightarrow \nu_\mu$ and
$\overline{\nu}_e \rightarrow \overline{\nu}_\mu$
oscillations. For baselines of a few thousand km
the ratio of rates
$N(\overline{\nu}_e \rightarrow \overline{\nu}_\mu) /
N(\nu_e \rightarrow \nu_\mu)$ is sensitive to the
sign of $\delta m^2$, and hence to the pattern of
neutrino masses (Fig.~\ref{fig:summary_cp}). With $10^{19}$ decays
and a 50~kt detector a unique and statistically
significant measurement of the neutrino mass spectrum
could be made. In addition, the $\nu_e \rightarrow \nu_\mu$
event rate is approximately proportional to
the parameter $\sin^2 2\theta_{13}$, which could therefore
be measured.
\begin{figure}
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\epsffile{summary_t13.eps}}
\caption{Limits on $\sin^2 2\theta_{13}$ that
would result from the absense of a $\nu_e \rightarrow \nu_\mu$
signal in a 10~kt detector 7400~km downstream of a
30~GeV neutrino factory in which there are $10^{20}$ and
$10^{21} \mu^+$ decays, followed by the same number of $\mu^-$ decays.
The limits are shown as a function of $\delta m^2_{32}$.
The impact of including backgrounds in the analysis is shown.
Note that
the unshaded band shows the $\delta m^2$ region favored by the
SuperK atmospheric neutrino deficit results.
Results are from Ref.~\ref{camp00}.
}
\label{fig:summary_t13}
\end{figure}
\begin{figure}
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\centerline{
\epsffile{summary_t13meas.eps}}
\caption{Precision with which the oscillation parameters
$\sin^2 \theta_{23}$ and $\sin^2 2\theta_{13}$ can be
measured in a 10~kt detector 7400~km downstream of a
30~GeV neutrino factory in which there are $10^{19}$, $10^{20}$, and
$10^{21} \mu^+$ decays.
Results are from Ref.~\ref{camp00}.
}
\label{fig:summary_precision}
\end{figure}
With higher beam intensities and/or higher beam energies the
physics potential of a neutrino factory is enhanced
(Fig.~\ref{fig:summary_all}).
In particular, as the intensity is increased to O($10^{20}$)
decays/year $\nu_e \rightarrow \nu_\tau$ oscillations might
be measured, and eventually \textsf{CP} violation in the lepton
sector observed if the large mixing angle MSW solution is the
correct description of the solar neutrino deficit.
Higher beam intensities would also allow smaller values of
$\sin^2 2\theta_{13}$ to be probed (Fig. ~\ref{fig:summary_t13}),
and higher precision
measurements of the oscillation parameters to be made.
An example of the improvement of measurement precision with
neutrino factory intensity is shown in
Fig.~\ref{fig:summary_precision} for the
determinations of $\sin^2 \theta_{23}$ and $\sin^2 2\theta_{13}$.
The physics program at detectors located close to the neutrino factory is
also compelling. The neutrino fluxes are four orders of magnitude
higher than those from existing beams. Such intense beams make experiments
with high precision detectors and low mass targets feasible for the first
time.Using these detectors and the unique ability of neutrinos to
probe
particular flavors of quarks will allow a precise measurement of the
individual light quark contents of the nucleon in both an isolated and
nuclear environment.
In addition,
neutrinos provide an elegant tool for probing the spin structure of
the nucleon and may finally enable resolution of the nucleon spin among
its partonic components.
The high event rates at a neutrino factory would
also enable a new generation of precision studies of electro-weak
and strong interaction parameters as well as
searches for exotic phenomena other than oscillations.
%In addition,
%neutrinos prove to be an elegant tool in probing the spin structure of
%the nucleon and may finally enable resolution of the nucleon spin among
%its partonic components.
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